Diffusion Characters of the Orbits in the Asteroid Motion

ZHOU Li-yong; SUN Yi-sui; ZHOU Ji-lin

Volume 22 Issue 7

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Article Navigation > Applied Mathematics and Mechanics > 2001 > 22(7): 719-728

ZHOU Li-yong, SUN Yi-sui, ZHOU Ji-lin. Diffusion Characters of the Orbits in the Asteroid Motion[J]. Applied Mathematics and Mechanics, 2001, 22(7): 719-728.

Citation:

ZHOU Li-yong, SUN Yi-sui, ZHOU Ji-lin. Diffusion Characters of the Orbits in the Asteroid Motion[J]. Applied Mathematics and Mechanics, 2001, 22(7): 719-728.

Citation:

ZHOU Li-yong, SUN Yi-sui, ZHOU Ji-lin. Diffusion Characters of the Orbits in the Asteroid Motion[J]. Applied Mathematics and Mechanics, 2001, 22(7): 719-728.

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Diffusion Characters of the Orbits in the Asteroid Motion

Department of Astronomy, Nanjing University, Nanjing 210093, P. R. China

Received Date: 2000-03-31
Rev Recd Date: 2001-02-13
Publish Date: 2001-07-15

Abstract

Abstract

A symplectic mapping is studied carefully. The exponential diffusion law in developed chaotic region and algebraic law in mixed region were observed. An area was found where the diffusion follows a logarithmic law. It is shown in the vicinity of an island, the logarithm of the escape time decreases linearily as the initial position moves away from the island. But when approaching close to the island, the escape time goes up very quickly, consistent with the superexponential stability of the invariant curve. When applied to the motion of asteroid, this mapping's fixed points and their stabilities give an explanation of the distribution of asteroids. The diffusion velocities in 4:3, 3:2 and 2:1 jovian resonances are also investigated.
- diffusion,
- symplectic mapping,
- asteroid

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References(10)

References

[1]	Meiss J D.Symplectic maps,variational principles,and transport[J].Rev Mod Phys,1992,64(3):795-848;Contopoulos G.Analysis and Modeling of Discrete Dynamical Systems[M].Netherlands;OPA,1998,35-90;Sun Y S,Fu Y N.Diffusion characters in a four-dimensional volume-preserving map[J].Cel Mech Dyn Astron,1999,73(4):249-258.
[2]	Nesvorny D,Ferraz-Mello S.On the asteroidal population of the first-order jovian resonances[J].Icarus,1997,130(2):247-258.
[3]	Froeschle C,Lega E.Analysis and Modeling of Discrete Dynamical Systems[M].Netherlands,OPA,1998,3-54;Hadjidemetriou J D.Analysis and Modeling of Discrete Dynamical Systems[M].Netherlands:OPA,1998:249-282.
[4]	Duncan M,Quiun T,Tremaine S.The long-term evolution of orbits in the solar system:a mapping approach[J].Icarus,1989,82(3):402-418.
[5]	Henon M,Petit J M.Series expansions for encounter-type solution of hills problem[J].Cel Mech,1986,38(2):67-100.
[6]	Hadjidemetriou J D.Predictability,Stability and Chaos in n-Body Dynamical Systems[M].Netherlands:Plenum Press,1991,157-175.
[7]	Lai Y C,Grebogi C,Blumel R.Algebraic decay and phase-space metamporphoses in microwave ionization of hydrogen rydberg[J].Phys Rev A,1992,45(12):8284-8287.
[8]	Morbidelli A,Giorgilli A.Chaos and diffusion in hamiltonian systems[M].France:Editions Frontiers,1995,65-112.
[9]	Evans N W,Tabachnik S.Possible long-lived asteroid belts in the inner solar system[J].Nature,1999,399:41-43.
[10]	Ferraz-Mello S,Michtchenko T A,Roig F.Determinant role of Jupiter's great inequality in the depletion of the hecuba gap[J].Astron J,1998,116(3):1491-1500.

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